1 numerical analyses of a viscid compressible ionic flow c. tulita, s.raghunathan, e. benard 1
TRANSCRIPT
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NUMERICAL ANALYSES OF AVISCID COMPRESSIBLE IONIC FLOW
C. Tulita, S.Raghunathan , E. Benard
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PLASMA FLOW CONTROL
OBJECTIVES
•Prevent Separation•Reduce Drag
PLASMA TECHNIQUES
•Corona Discharge
•Glow Discharge
By creating an important electriccharge distribution in a particular region
of the flow.
It occurs near sharp points, whereit creates a localized electric fieldgreater than the breakdown electric field of the medium surrounding it.
It operates at the Stoletow point, atwhich the energy cost of an ion-electron
pair is the minimum theoretically possible.
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Case: M=0.147, Re=2.8106, =0°
CORONA DISCHARGE EFFECT ON AN AEROFOIL IN SUBSONIC FLOW
Local electric field
Electricpotential
Plasma on
Plasma off
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Aerofoil wallWake cut Wake cut
NUMERICAL STRATEGY
C-Grid TransformationCFD mesh
Electro-dynamic grid
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cii ,
gradE
0, iiic vkE
0, iiv
0
ngradn
kV25
kV10
ELECTRODYNAMIC PROBLEM
mmAJvEk cc /40
Poisson equation
Conservation of the electric charge
Patankar control-volume method
Leger-Moreau-Touchard 2001
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CORONA EXPERIMENTAL CORRELATIONAT ANODE. Peek (1929) & Cobine(1958)
The initiating voltage for corona
MVa
daEV si
ln
m
MV
amEs
0308.0
11.3
1;67.0m The empirical surface roughness factor
11,298298
atmpKTT
p The relative atmospheric density factor
rVV i 0
dar
Plasma Active Volume
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ELECTRODYNAMIC RESULTATS
sE
BE
cm
kVE
cm
kVE
B
s
27
31
ijjiij EEET
2
2
Electric potential
Electric field
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0
0
0
,,
,,
,,,
ijijiit
jijijjiti
iit
vqhve
pvvv
v
RTp
FLUIDE PROBLEM
e , iv
iv 0jijn 0, iine
Inflow: given and extrapolated
Outflow: given and
T
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MASS-AVERAGED NAVIER-STOKES EQUATIONS IN TWO DIMENSIONAL
CONSERVATION FORM
0
y
G
x
F
t
U
e
v
uU
~
~
~
y
TkkuTvTe
Tv
Tvu
v
G
tyxyxyxyyy
yyy
yxyxyx
~)(~~~~~~~
~~~
~~~~
~
2
x
TkkvTuTe
Tvu
Tu
u
F
txyyxyxxxx
xyxyxy
xxx
~)(~~~~~~~
~~~~
~~~
~
2
2
2
~2
~~~~
~~~~~~
~2
~~~~
vy
v
y
v
x
up
vux
v
y
u
ux
u
y
v
x
up
yy
yxyxxyxy
xx
2
~~~)1(
22 vuep
TC
vue
v~~2
~~~~
22
02
1
3
2~3
2~~
,
,,,
ik
tjjijij
ijijkkijjitji
Kvvvv
Kuuuuu
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Tow dimensional thin-layer, mass-averaged Navier-Stokes code
NUMERICAL METHOD
Upwind implicit MacCormack predictor/corrector cell-centered finite-volume method
Flux Splitting method of Van Leer
Mulder’s continuous differentiable flux limiter
Gauss-Seidel line relaxation iterative procedure
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Modified version of the Baldwin-Lomax turbulence model,using a non-linear formulation of the wall region anisotropy
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AERODYNAMIC RESULTATS
Case: M=0.147, Re=2.8106, =0°
Plasma off Plasma on
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SKIN FRICTION COEFFICIENT
Plasma onPlasma off
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PRESSURE COEFFICIENT DISTRIBUTIONS
Plasma onPlasma off
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CONCLUDING REMARKS
Reduces drag
Enhance the mass and heat transfer between the aerofoil and surrounding flow 13
SUBSONIC REGIME
CORONA DISCHARGE TECHNIQUE
Prevents separation
The ionic charge distribution depends strongly on:
•The anode electrode radius•The empirical surface roughness factor•The relative atmospheric density factor•The potential difference between anode and cathode
PLASMA CHEMISTRY FROM THE ACTIVE VOLUME
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Electric fieldElectric potential
mmAJvEk cc /3
Possible Electric Results
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